Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample1.2s (38.5%)

Results

935.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 47 to 38 computations (19.1% saved)

simplify235.0ms (7.6%)

Algorithm

1×	egg-herbie

Rules

2682×	`fma-neg_binary64`
690×	`times-frac_binary64`
636×	`fma-def_binary64`
533×	`sub-neg_binary64`
432×	`distribute-rgt-neg-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	25	19
2	45	17
3	65	17
4	78	17
5	89	17
6	129	17
7	180	17
8	288	17
9	497	17
10	671	17
11	811	17
12	976	17
13	1611	17
14	3407	17
15	3743	17
16	3727	17
17	3787	17
18	3819	17
19	3887	17
20	3898	17
21	4186	17
22	4220	17
23	4236	17
24	4236	17
25	4236	17
26	6212	17

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.9b	(/.f64 (.f64 6 (-.f64 x 1)) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))
▶	0.9b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

Compiler

Compiled 83 to 64 computations (22.9% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
✓	0.1b	(fma.f64 6 x -6)
✓	0.8b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

series23.0ms (0.7%)

Counts

3 → 18

Calls

3 calls:

17.0ms	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
4.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
1.0ms	(fma.f64 6 x -6)

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 49

Calls

3 calls:

2.0ms	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
0.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
0.0ms	(fma.f64 6 x -6)

simplify106.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

492×	`div-sub_binary64`
426×	`fma-neg_binary64`
384×	`*-commutative_binary64`
348×	`distribute-rgt-in_binary64`
336×	`distribute-lft-in_binary64`

Counts

67 → 64

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	1136
1	110	1034
2	285	1034
3	751	1025
4	2413	1025
5	3154	1025
6	4752	1025
7	4942	1025

prune56.0ms (1.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	58	6	64
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	60	6	66

Error

Counts

66 → 6

Alt Table

Status	Error	Program
▶	0.9b	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
	22.6b	(/.f64 (cbrt.f64 (pow.f64 (fma.f64 6 x -6) 3)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
	33.5b	6
	1.5b	(/.f64 (/.f64 (fma.f64 6 x -6) (*.f64 (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))) (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
	34.5b	(/.f64 (sqrt.f64 (fma.f64 6 x -6)) (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (sqrt.f64 (fma.f64 6 x -6))))
	1.0b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))

Compiler

Compiled 1393 to 1008 computations (27.6% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 -1 (fma.f64 4 (sqrt.f64 x) x))
✓	0.0b	(fma.f64 4 (sqrt.f64 x) x)
✓	0.1b	(fma.f64 -6 x 6)
✓	0.8b	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))

series32.0ms (1%)

Counts

4 → 20

Calls

4 calls:

19.0ms	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
5.0ms	(-.f64 -1 (fma.f64 4 (sqrt.f64 x) x))
5.0ms	(fma.f64 4 (sqrt.f64 x) x)
2.0ms	(fma.f64 -6 x 6)

rewrite11.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
32×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
15×	`times-frac_binary64`
9×	`prod-diff_binary64`

Counts

4 → 90

Calls

4 calls:

3.0ms	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
3.0ms	(-.f64 -1 (fma.f64 4 (sqrt.f64 x) x))
0.0ms	(fma.f64 4 (sqrt.f64 x) x)
0.0ms	(fma.f64 -6 x 6)

simplify101.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

987×	`div-sub_binary64`
834×	`fma-neg_binary64`
353×	`cancel-sign-sub-inv_binary64`
292×	`associate-l_binary64`
221×	`fma-def_binary64`

Counts

110 → 109

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	131	2105
1	232	1777
2	663	1694
3	2447	1692
4	4275	1684
5	5888	1684

prune96.0ms (3.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	109	6	115

Error

Counts

115 → 6

Alt Table

Status	Error	Program
✓	0.9b	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
	22.6b	(/.f64 (cbrt.f64 (pow.f64 (fma.f64 6 x -6) 3)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
	33.5b	6
	1.5b	(/.f64 (/.f64 (fma.f64 6 x -6) (*.f64 (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))) (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
	34.5b	(/.f64 (sqrt.f64 (fma.f64 6 x -6)) (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (sqrt.f64 (fma.f64 6 x -6))))
▶	1.0b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))

Compiler

Compiled 2637 to 1848 computations (29.9% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
✓	0.0b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))
	0.1b	(fma.f64 6 x -6)
✓	0.9b	(/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6))

series22.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

13.0ms	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))
9.0ms	(/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6))

rewrite19.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 107

Calls

2 calls:

4.0ms	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))
2.0ms	(/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6))

simplify145.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

710×	`distribute-rgt-in_binary64`
694×	`distribute-lft-in_binary64`
455×	`div-sub_binary64`
283×	`associate-/l*_binary64`
276×	`+-commutative_binary64`

Counts

113 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	105	3414
1	179	3099
2	493	3072
3	1384	3057
4	3517	3057
5	4145	3057
6	5164	3057

prune138.0ms (4.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	169	1	170
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	170	6	176

Error

Counts

176 → 6

Alt Table

Status	Error	Program
✓	0.9b	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
	22.6b	(/.f64 (cbrt.f64 (pow.f64 (fma.f64 6 x -6) 3)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
	33.5b	6
▶	1.5b	(/.f64 (/.f64 (fma.f64 6 x -6) (*.f64 (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))) (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
✓	1.0b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))
	34.3b	(exp.f64 (neg.f64 (log.f64 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))))

Compiler

Compiled 4450 to 3339 computations (25% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 (fma.f64 6 x -6) (*.f64 (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))) (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
✓	0.2b	(*.f64 (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
✓	0.3b	(cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
✓	0.9b	(/.f64 (fma.f64 6 x -6) (*.f64 (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))

series115.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

48.0ms	(/.f64 (fma.f64 6 x -6) (*.f64 (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
29.0ms	(*.f64 (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
23.0ms	(cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
15.0ms	(/.f64 (/.f64 (fma.f64 6 x -6) (*.f64 (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))) (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

rewrite30.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64`
53×	`add-sqr-sqrt_binary64`
45×	`*-un-lft-identity_binary64`
45×	`add-cube-cbrt_binary64`
43×	`cbrt-prod_binary64`

Counts

4 → 152

Calls

4 calls:

6.0ms	(/.f64 (/.f64 (fma.f64 6 x -6) (*.f64 (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))) (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
6.0ms	(*.f64 (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
4.0ms	(/.f64 (fma.f64 6 x -6) (*.f64 (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
1.0ms	(cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

simplify230.0ms (7.4%)

Algorithm

1×	egg-herbie

Rules

459×	`fma-def_binary64`
434×	`associate-/l/_binary64`
384×	`associate-/l*_binary64`
361×	`associate-/r/_binary64`
321×	`associate-l_binary64`

Counts

164 → 245

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	184	7052
1	346	6374
2	1034	5394
3	3675	4989
4	4607	4898
5	4974	4898
6	4936	4898

prune305.0ms (9.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	284	1	285
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	286	5	291

Error

Counts

291 → 5

Alt Table

Status	Error	Program
✓	0.9b	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
	1.4b	(/.f64 (/.f64 (fma.f64 6 x -6) (pow.f64 (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) 5/2)) (sqrt.f64 (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	22.6b	(/.f64 (cbrt.f64 (pow.f64 (fma.f64 6 x -6) 3)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
	33.5b	6
✓	1.0b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))

Compiler

Compiled 11642 to 8259 computations (29.1% saved)

regimes96.0ms (3.1%)

Accuracy

Total 0.2b remaining (92.4%)

Threshold costs 0.2b (92.4%)

Counts

46 → 1

Compiler

Compiled 1851 to 1452 computations (21.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	13	17
2	17	17
3	19	17
4	20	17
5	20	17

end91.0ms (2.9%)

Compiler: Compiled 98 to 77 computations (21.4% saved)

Details

analyze4.0ms (0.1%)

sample1.2s (38.5%)

simplify235.0ms (7.6%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series23.0ms (0.7%)

rewrite4.0ms (0.1%)

simplify106.0ms (3.4%)

prune56.0ms (1.8%)

localize7.0ms (0.2%)

series32.0ms (1%)

rewrite11.0ms (0.4%)

simplify101.0ms (3.3%)

prune96.0ms (3.1%)

localize11.0ms (0.4%)

series22.0ms (0.7%)

rewrite19.0ms (0.6%)

simplify145.0ms (4.7%)

prune138.0ms (4.5%)

localize11.0ms (0.4%)

series115.0ms (3.7%)

rewrite30.0ms (1%)

simplify230.0ms (7.4%)

prune305.0ms (9.9%)

regimes96.0ms (3.1%)

simplify3.0ms (0.1%)

end91.0ms (2.9%)

Profiling